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# Three married couples have bought 6 seats in a row for a

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Manager
Joined: 14 Dec 2004
Posts: 119
Followers: 1

Kudos [?]: 9 [0], given: 0

Three married couples have bought 6 seats in a row for a [#permalink]  13 Jan 2005, 19:09
Three married couples have bought 6 seats in a row for a performance of a musical comedy.

1. In how many ways can they be seated?
2. In how many ways can they be seated if each couple is to sit together with the husband to the left of the wife?
3. In how many ways can they be seated if each couple is to sit together?
4. In how many ways can they be seated if all the men are to sit together and all the women are to sit together?
Senior Manager
Joined: 22 Jun 2004
Posts: 394
Location: Bangalore, India
Followers: 1

Kudos [?]: 2 [0], given: 0

Re: counting [#permalink]  13 Jan 2005, 23:28

(1) 6 people in 6 seats => 6! = 720

(2)There is a definite order contsraint that husband is to the left of wife. Thus, 3 couples can seat in 3! = 6 ways.

(3)3 couples can seat in 3! ways and each couple can themselves change seats in 2! ways.

Thus, the totall number of ways = 3! * 2! *2! * 2! = 48

(4)3 Men can seat 3! ways in 3 seats.
3 Women can seat 3! ways in 3 seats.
Men and women as two packs can occupy the seats in 2! ways (Leftmost 3 seats women or rightmost 3 seats women).

=> the total number of ways = 2! * 3! * 3! = 72

cloaked_vessel wrote:
Three married couples have bought 6 seats in a row for a performance of a musical comedy.

1. In how many ways can they be seated?
2. In how many ways can they be seated if each couple is to sit together with the husband to the left of the wife?
3. In how many ways can they be seated if each couple is to sit together?
4. In how many ways can they be seated if all the men are to sit together and all the women are to sit together?

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Director
Joined: 07 Jun 2004
Posts: 617
Location: PA
Followers: 3

Kudos [?]: 263 [0], given: 22

1. 6!

2. 3!

3. 3! * (2!)^3

4. 3! * 3! * 2!
Manager
Joined: 14 Dec 2004
Posts: 119
Followers: 1

Kudos [?]: 9 [0], given: 0

correct:

720,

6,

48,

72
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